Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#15690276 | C2 | semidirect |
| 2. C2×#20259328 | C2 | semidirect |
| 3. #27133239 | C2 | semidirect |
| 5. #27132910 | C2 | semidirect |
| 6. #27132893 | C2 | semidirect |
| 7. #27132671 | C2 | semidirect |
| 8. #27132667 | C2 | semidirect |
| 9. #427×C191 | C2 | semidirect |
| 18. C2×#15690270 | C22 | semidirect |
| 19. C2×C8×D191 | C22 | semidirect |
| 25. #20259302 | C22 | semidirect |
| 28. #20259245 | C22 | semidirect |
| 33. #107×C191 | C22 | semidirect |
| 34. #106×C191 | C22 | semidirect |
| 62. C2×C8×C191 | D4 | semidirect |
| 120. C191 | #3057 | semidirect |
| 128. #427 | D191 | semidirect |
| 152. #107 | C2×D191 | semidirect |
| 153. #106 | C2×D191 | semidirect |
| 180. C2×C8 | D764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15690276 | 2 |
| C2×#20259328 | 2 |
| #27133239 | 2 |
| #27133232 | 2 |
| #27132910 | 2 |
| #27132893 | 2 |
| #27132671 | 2 |
| #27132667 | 2 |
| #427×C191 | 2 |
| #3057 | 191 |